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Please note that all times are shown in the time zone of the conference. The current conference time is: 30th Nov 2022, 08:57:48pm CET

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Session Overview
MS 20b: Fluid Applications of High-Order Finite Element Methods
Thursday, 15/July/2021:
4:00pm - 6:00pm

Session Chair: Will Pazner
Session Chair: Per-Olof Persson
Session Chair: Matthew Joseph Zahr
Virtual location: Zoom 6

Session Abstract

Modern computational architectures have spurred recent interest in the use of a high-order finite element and discontinuous Galerkin methods for problems in computational fluid dynamics (CFD). These methods often feature low dissipation, compact stencils, and high arithmetic intensity, making them well-suited for accelerators and GPU-based architectures. Such methods have seen success when applied to challenging CFD problems such as large eddy simulation and under-resolved turbulence.

This session aims to bring together researchers from the broad field of high-order finite element methods for computational fluid dynamics in order to discuss recent developments in the areas of discretizations, solvers, and software. Specific topics of interest include shock capturing and tracking methods, stable and robust discretizations, efficient solvers and time integration (implicit, explicit, and IMEX), matrix-free algorithms, and algorithms for advanced computer architectures.

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4:00pm - 4:30pm

Applications of a Moving Discontinuous Galerkin Method with Interface Condition Enforcement

Andrew Kercher, Andrew Corrigan, David Kessler

Naval Research Laboratory, United States of America

The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to high-speed compressible flows. The method uses a weak formulation that separately enforces a conservation law and the corresponding interface condition while treating the discrete geometry as a variable. By satisfying the weak form, MDG-ICE implicitly fits discontinuous interfaces, including shocks, material interfaces, and derivative discontinuities, and resolves sharp, but smooth, gradients using anisotropic curvilinear r-adaptivity. The method is shown to fit a priori unknown interfaces, including curved interface geometries as well as non-trivial intersecting interface topologies and to automatically adapt high-order shape representations anisotropically in order to accurately resolve viscous shocks and boundary layers. High-order convergence is demonstrated for problems involving discontinuous interfaces as well as problems involving sharp boundary layers. The accuracy and performance MDG-ICE, in comparison to shock capturing methods, is assessed in the context of multi-dimensional high-speed flows.

4:30pm - 5:00pm

Higher order space-time discretizations of the Navier-Stokes equations on evolving domains

Mathias Anselmann, Markus Bause

Helmut Schmidt University, Germany

A higher order space-time finite element approach for solving the nonstationary, incompressible Navier-Stokes equations on evolving domains is presented.

The physical fluid domain is embedded into a fixed computational mesh such that arbitrary intersections of the moving domain’s boundaries with the background mesh occur. Cut finite element techniques are applied to capture the intersections. The key ingredients of the approach are the weak formulation of Dirichlet boundary conditions by Nitsche’s method, the flexible and efficient integration over all types of intersections of cells by moving boundaries and the spatial extension of the discrete physical quantities to the entire computational background mesh. To prevent spurious oscillations caused by irregular intersections of mesh cells a penalization is used. Thereby the stability of the approach is ensured and an implicit extension of the physical flow quantities to the computational domain is provided. The convergence and stability of this approach is studied and evaluated by various numerical examples, including benchmarks problems for fluid flow.

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